Some numerical methods have been introduced for the simulation of the DPCM in [1]} and implemented in the code CALIPSO. For the simplified two-species DPCM on a fixed domain, the numerical scheme is described and analyzed in [2]}. It is based on a Scharfetter-Gummel approximation of the linear drift-diffusion fluxes.
The main change we made when designing the new model (we will call in the sequel vDPCM) relies on the new definition of the fluxes of cations which are now nonlinear with respect to the densities of cations. For the approximation of this new flux, we consider an extension of the SQRA (SQuare-Root Approximation) introduced in [3]}. The scheme will be introduced and analyzed in further work.
